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Using Cramer's Rule to find needed equations

  1. Dec 18, 2012 #1
    1. The problem statement, all variables and given/known data
    I am finding the minimum coefficient μ between tires and road so that cars do not slide off. I have my equations for ƩFy and ƩFx and I know μ = [fs]/[/N]

    So I would need to use cramer's rule on my equations to find fs and N.

    But I am not sure how to use cramer's rule for my equations.


    2. Relevant equations
    ƩFx = Nsinθ -fscosθ = mv2/r
    ƩFy = Ncosθ + fssinθ = mg

    3. The attempt at a solution
    I actually already have the answer but im not sure how to use cramer's to get to it.

    fs = m(gsinθ-v2/r*cosθ)

    N = m(v2/r*sinθ+gcosθ)
     
  2. jcsd
  3. Dec 18, 2012 #2

    haruspex

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    At a guess (which I should not be needing to do!) the car is negotiating a bend radius r, banked at angle theta (in the helpful direction).
    Sure about the sign of fs in those? Or is this calculating the minimum speed?
    You have two equations and two unknowns. You're accustomed to dealing with pairs of simultaneous equations, I trust.
     
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